This book is written to introduce computer simulations to undergraduate
college students, freshmen to seniors, in STEM fields. The book starts
with concepts from Basic Mathematics: Geometry, Algebra and Calculus,
Properties of Elementary Functions (Polynomials, Exponential, Hyperbolic
and Trigonometric Functions) are studied and simple differential
equations representing these functions are derived. Numerical
approximations of first and second order differential equations are
studied in terms of finite differences on uniform grids. Computer
solutions are obtained via recursive relations or solutions of
simultaneous algebraic equations. Comparisons with the exact solutions
(known a priori) allow the calculations of the error due to
discretization. After the students build confidence in this approach,
more problems where the solutions are not known a priori are tackled
with applications in many fields. Next, the book gradually addresses
linear differential equations with variable coefficients and nonlinear
differential equations, including problems of bifurcation and
chaos.Applications in Dynamics, Solid Mechanics, Fluid Mechanics, Heat
Transfer, Chemical Reactions, and Combustion are included. Biographies
of 50 pioneering mathematicians and scientists who contributed to the
materials of the book are briefly sketched, to shed light on the history
of these STEM fields.Finally, the main concepts discussed in the book,
are summarized to make sure that the students do not miss any of them.
Also, references for further readings are given for interested readers.
